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nth Term of A.P

If C 0, C 1, ...

Question

If $C_{0}, C_{1}, C_{2}, . . . . . . . . . . . C_{n}$ are the Binomial coefficients in the expansion $(1 + x)^{n} .$ ‘n’ being even, then $C_{0} + (C_{0} + C_{1}) + (C_{0} + C_{1} + C_{2}) + . . . . . . . . . (C_{0} + C_{1} + C_{2} + . . . . . + C_{n - 1})$ =is equal to

A

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B

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C

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D

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Solution

The correct option is B
$S u m = {C_{0} + (c_{1} + c_{2} + . . . . . + c_{n - 1})} + = {(c_{0} + c_{1}) +$ $(c_{0} + c_{1} + . . . . . . + c_{n - 2})} + {(c_{0} + c_{1} + c_{2}) + (c_{0} + c_{1} + . . . . . + c_{n - 3})} + . . . . . . . \to (\frac{n}{2})$
$T e r m = (c_{0} + c_{1} + . . . . . c_{n}) \times \frac{n}{2} = n {.2}^{n - 1}$

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Similar questions

C_{0}, C_{1}, C_{2}, . . . . . . . . . . C_{n}

are the binomial coefficients in the expansion of

(1 + x)^{n}

. n being even, then

C_{0} + (C_{0} + C_{1}) + (C_{0} + C_{1} + C_{2}) + . . . . . . . . + (C_{0} + C_{1} + C_{2} + . . . . . . . . . + C_{n - 1})

C_{0}, C_{1}, C_{2} . . . . . . . . . . ., C_{n}

are the binomial coefficient in the expansion of

(1 + x)^{n}, n

being even, then

C_{0} + (C_{0} + C_{1}) + (C_{0} + C_{1} + C_{2}) + . . . . . . . + (C_{0} + C_{1} + C_{2} + . . . . . . . . + C_{n - 1})

c_{0}, c_{1}, c_{2}, . . . . c_{n}

denote the coefficients in the expansion of

(1 + x)^{n}

c_{0} + \frac{c_{1}}{2} + \frac{c_{2}}{3} + . . . . . + \frac{c_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}

c_{0}, c_{1}, c_{2}, . . . . . . . c_{n}

denote the coefficients in the expansion of

{(1 + x)}^{n}

c_{0} + \frac{c_{1}}{2} + \frac{c_{2}}{3} + . . . . . . + \frac{c_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}

C_{0}, C_{1}, C_{2}, \dots, C_{n}

are Binomial Coefficient in the expansion of

{(1 + x)}^{n}

C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + \dots + \frac{C_{n}}{n + 1}

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